Let a and b be two elements of a group G such that a has order 3, b has order 2, and bab-1= a-1. Prove that ab has order 6 by showing none of (ab) 2 , (ab) 3 , . . . , (ab) 5 are equal to e, but (ab) 6 = e. Given an example of a group and elements a and b such that a has order 3, b has order 2, and bab-1= a-1.